Question:
Solve the following system of equations for x and y:
1. 3x + 2y = 8
2. 2x - y = 4
Solution:
1. 3x + 2y = 8
2. 2x - y = 4
We can use either the substitution method or the elimination method. Let's use the elimination method to solve for x and y:
Step 1: Multiply Equation 2 by 2 to make the coefficients of y in both equations equal:
2 * (2x - y) = 2 * 4
4x - 2y = 8
Now, the system becomes:
1. 3x + 2y = 8
2. 4x - 2y = 8
Step 2: Add both equations to eliminate y:
(3x + 2y) + (4x - 2y) = 8 + 8
7x = 16
Step 3: Solve for x:
x = 16 / 7
Step 4: Substitute the value of x into either of the original equations to solve for y. Let's use Equation 1:
3 * (16 / 7) + 2y = 8
48/7 + 2y = 8
Step 5: Solve for y:
2y = 8 - 48/7
2y = (56 - 48)/7
2y = 8/7
y = 4/7
So, the solution to the system of equations is x = 16/7 and y = 4/7.
